Recent content by yayMath

  1. Y

    How can I create a power series expansion for x^2 / (1+x^2)?

    I was wondering how to create a power series expansion for the function x^2 / (1+x^2)... I've tried using the geometric series, but somehow i got stuck. thanks.
    • yayMath
    • Thread
    • Expansion Power Power series Series Series expansion
    • Replies: 2
    • Forum: Calculus
  2. Y

    Is There a Continuous Function Satisfying These Conditions?

    so, I've gotten to the point at which g(x) = f(x) - f(x+2/5) does nto equal zero for any x in [0, 3/5]... finding a form for g(x) is not difficult, but the constraint f(0) = f(1), i have no idea how to include it.
  3. Y

    Is There a Continuous Function Satisfying These Conditions?

    Function is continuous Yes, unfortunately, the function is continuous.
  4. Y

    Is There a Continuous Function Satisfying These Conditions?

    ... f(0)=f(1) but for all x in [0,3/5] f(x) does not equal f(x+2/5) ?
  5. Y

    Does the Function f(x) Have a Fixed Point If f'(x) ≥ 2?

    Hi, I need to prove that f(x) has a fixed point, given that f'(x) >= 2 for all x. my problem is that I've reached the part in which g(x) = f(x) - x and g'(x) = f'(x) - 1 and therefore g'(x) >= 1 but now I'm completely stuck. I knwo that I need to use the mean value theorem, but i just...
    • yayMath
    • Thread
    • Fixed point Function Point
    • Replies: 2
    • Forum: Calculus
  6. Y

    Proving the Existence of Fixed Points in Monotone Increasing Functions

    I was reading through that proof, and I did not understand how "Hence if g(0) = c>0 say, and n < a < n+1, then g(-n-1) < 0" this step came to be? thanx
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